Abstract
Tremendous ongoing theory efforts are dedicated to developing new methods for quantum chromodynamics (QCD) calculations. Qualitative rather than incremental advances are needed to fully exploit data that are still to be collected at the LHC. The maximally supersymmetric Yang–Mills theory, [Formula: see text] super Yang–Mills (sYM), shares with QCD the gluon sector, which contains the most complicated Feynman graphs but also has many special properties and is believed to be solvable exactly. It is natural to ask what we can learn from advances in [Formula: see text] sYM for addressing difficult problems in QCD. With this in mind, I review several remarkable developments and highlights of recent results in [Formula: see text] sYM. This includes all-order results for certain scattering amplitudes, novel symmetries, surprising geometrical structures of loop integrands, novel tools for the calculation of Feynman integrals, and bootstrap methods. While several insights and tools have already been carried over to QCD and have contributed to state-of-the-art calculations for LHC physics, I argue that there is a host of further fascinating ideas waiting to be explored.
Highlights
Some readers might ask whether studies in N = 4 super Yang–Mills (sYM), rewarding they may be in their own right, are not somewhat esoteric, in the sense that they seem far removed from the gritty calculations of “real” quantum chromodynamics (QCD)
Looking at super Yang–Mills theory offers a lot of insight into how one can deal with the problems in QCD.”
Can we develop methods to systematically compute Feynman integrals in QCD? Can we compute physical quantities without explicitly evaluating Feynman diagrams? How can our calculations benefit from knowledge of physical properties of the underlying quantum field theory (QFT), such as unitarity, space-time symmetries, and conformal invariance? Can we compute finite physical quantities in a way that avoids infrared singularities? Which properties of QCD scattering amplitudes are governed by Wilson loops?
Summary
Another goal is to point out where this research has already led to a transfer of knowledge to QCD. New insights into N = 4 sYM have already led to novel tools for QCD and are being used for cutting-edge calculations relevant to LHC physics. . .] is calculating QCD amplitudes, the concept design of various ideas and methods is carried out in supersymmetric theories, which provide an excellent testing ground. Looking at super Yang–Mills theory offers a lot of insight into how one can deal with the problems in QCD.”. With this in mind, here are a few important, concrete questions: Scattering amplitudes: key ingredients of cross sections, analogous to probability amplitudes in quantum mechanics. Can we develop methods to systematically compute Feynman integrals in QCD? Can we compute physical quantities without explicitly evaluating Feynman diagrams? How can our calculations benefit from knowledge of physical properties of the underlying QFT, such as unitarity, space-time symmetries, and conformal invariance? Can we compute finite physical quantities in a way that avoids infrared singularities? Which properties of QCD scattering amplitudes are governed by Wilson loops?
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